Different settings in blendfile
Those mapping settings will only appear if you are NOT using nodes to define your material in Blender Internal. Uncheck the button marked in red on the material tab to get the settings back as they are in the first screenshot:

It makes sense, as you would - when using nodes - drop in a mapping node to the node graph to do the same thing. That's why the panels (and many other options) disappear.
Edit
Regarding the HDRI, the ability to show an HDRI directly in the Viewport has been added to Blender in 2.77, you can get the latest release (currently 2.77a) on the Blender website: http://www.blender.org. If you want the HDRI to also reflect on the objects, you'll need a development build from https://builder.blender.org/download/
Here is a screenshot taken from Blender 2.77a:

and this is the same scene in the current development build: